Designing an Adhesive Pillar Shape with Deep Learning-Based Optimization

Over the past decades, significant effort has been made to improve the adhesive properties of adhesive pillars, by searching for pillar shapes with optimized interfacial stress distribution. However, the shape optimizations in the previous studies are conducted by considering specific pillar forms with a few parameters, hence with limited design space. In this study, we present a framework to find a free-form optimized adhesive pillar shape out of extensive design space. We generate 200 000 different shapes of adhesive pillars based on the Bézier curve with a few control points by considering two distinct edge shapes, sharp and truncated edges, to account for the limitation in the realistic manufacturing resolution. The resulting interfacial stress distributions from numerical simulations are used to train deep neural networks for each edge type. Our deep learning model shows greater than 99% classification accuracy on a limited data set with orders of magnitude speedup in computation time compared to finite element analyses. On the basis of the trained neural network, we conduct genetic optimization by maximizing a fitness function that prefers the uniform interfacial stress distribution with neither stress peak nor singularity. The optimized adhesive pillar shape is composed of smoothly mixed convex and concave parts and shows improved uniformity in the interfacial stress distribution. Our study also demonstrates that the deep learning can be used for nonparametric curve optimization task with diverse fitness function.